What are the rules of total ordering?

Total ordering says that the following rules must be satisfied:
1.Irreflexive)For no object o does o come before o.
2.Trichotomy)For any two objects o1 and o2,one and only one of the following holds true: o1 comes before o2,o1 comes after o2,or o1 equals o2.
3.Transitivity)If o1 comes before o2 and o2 comes before o3,then o1 comes before o3.